Thermal Instability and Photoionized X-Ray Reflection in Accretion Disks

We study the illumination of accretion disks in the vicinity of compact objects by an overlying X-ray source. Our approach differs from previous works of the subject in that we relax the simplifying assumption of constant gas density used in these studies; instead we determine the density from hydrostatic balance which is solved simultaneously with the ionization balance and the radiative transfer in a plane-parallel geometry. We calculate the temperature profile of the illuminated layer and the reprocessed X-ray spectra for a range of physical conditions, values of photon index Γ for the illuminating radiation, and the incident and viewing angles. In accordance with some earlier studies, we find that the self-consistent density determination makes evident the presence of a thermal ionization instability well known in the context of quasar emission line studies. The main effect of this instability is to prevent the illuminated gas from attaining temperatures at which the gas is unstable to thermal perturbations. Thus, in sharp contrast to the constant density calculations that predict a continuous and rather smooth variation of the gas temperature in the illuminated material, we find that the temperature profile consists of several well defined thermally stable layers. Transitions between these stable layers are very sharp and can be treated as discontinuities as far as the reprocessed spectra are concerned. In particular, the uppermost layers of the X-ray illuminated gas are found to be almost completely ionized and at the local Compton temperature (~107-108 K); at larger depths, the gas temperature drops abruptly to form a thin layer with T ~ 106 K, while at yet larger depths it decreases sharply to the disk effective temperature. For a given X-ray spectral index, this discontinuous temperature structure is governed by just one parameter, A, which characterizes the strength of the gravitational force relative to the incident X-ray flux. We find that most of the Fe Kα line emission and absorption edge are produced in the coolest, deepest layers, while the Fe atoms in the hottest, uppermost layers are generally almost fully ionized, hence making a negligible contribution to reprocessing features in the ~6.4-10 keV energy range. We also find that the Thomson depth of the top hot layers is pivotal in determining the fraction of the X-ray flux which penetrates to the deeper cooler layers, thereby affecting directly the strength of the Fe line, edge and reflection features. Due to the interplay of these effects, for Γ ≲ 2, the equivalent width (EW) of the Fe features decreases monotonically with the magnitude of the illuminating flux, while the line centroid energy remains at 6.4 keV. We provide a summary of the dependence of the reprocessing features in the X-ray reflected spectra on the gravity parameter A, the spectral index Γ, and other parameters of the problem. We emphasis that the results of our self-consistent calculations are both quantitatively and qualitatively different from those obtained using the constant density assumption. Therefore, we propose that future X-ray reflection calculations should always utilize hydrostatic balance in order to provide a reliable interpretation of X-ray spectra of active galactic nuclei and galactic black hole candidates.